Introduction

This analysis explores the relationships of agricultural commodity loss, at a county level, from 1989-2015, for the 26 county region of the Palouse, in Washington, Idaho, and Oregon. Here we explore the entire range of commodities and damage causes, identifying the top revenue loss commodities and their most pertinent damage causes - as indicated from the USDA’s agricultural commodity loss insurance archive.

In Phase 3, we perform mixed modeling analysis using a two-step hurdle technique, for apples, wheat, cherries, and dry peas, specifically for a selected set of damage causes. The following analysis builds on Phases 1 and 2, steps 1-8.

Step 9. Individual Commodity Mixed Model Analysis. In Step 9, we perform a mixed modeling analysis, using a two step hurdle model technique to address zero-inflated data.

Step 9: Hurdle Mixed Models

Hurdle model techniques allow us to address zero inflated datasets, by first running a logstical regression model to determine the probability of zeros occuring. Then we use the non-zero values in a separate, mixed model. In this instance, we use county as a random effect.

In our two part hurdle model, we identify zero values - that is, counties and years that have zero loss for particular damage causes for apples. Previously we removed counties that we have determined have no apples being grown - based on known crop yield data. The counties we are identifying are those where we KNOW apples are being grown, but in some instances, there are no loss claims being filed in particular years.

As such, these are not missing data, but actual zero values that we do not want to exclude from our model. However we want to be able to use a normalized distribution that is not positively skewed/zero inflated.


Hurdle Model - APPLES

Here we run our hurdle technique for APPLES, using a generalized linear model with a binomal function to delineate between zero and non-zero values. Given this model, Is our data normally distributed? What (if any) outliers exist? Are residuals well distributed - indicating normality?

##          llh      llhNull           G2     McFadden         r2ML 
## -294.4881431 -423.9973502  259.0184142    0.3054482    0.3371061 
##         r2CU 
##    0.4557171
## 
##  Hosmer and Lemeshow goodness of fit (GOF) test
## 
## data:  alllevs2_apples$non_zero, fitted(m1)
## X-squared = 8.3228, df = 8, p-value = 0.4026

FIGURE 12: Apples Non-zero Goodness of fit hoslem test


Now plot this Apples zero/non-zero bionomal model to see outliers and the zeros vs non-zeros.


FIGURE 13: Apples zero/non-zero bionomal model to see outliers and zeros values vs non-zero values.

##                            GVIF Df GVIF^(1/(2*Df))
## year                       1.16 14           1.005
## damagecause            36115.35  5           2.856
## county                 14626.71  6           2.224
## damagecause:county 101372467.97 30           1.360

FIGURE 14: Apples multi-collinearity test for our binomal model.


##                                          pvalue
## (Intercept)                        0.0295511713
## year2012                           0.0023203939
## year2014                           0.0269850901
## year2015                           0.0168428603
## damagecauseFreeze                  0.0193224383
## damagecauseFrost                   0.0004283115
## countyBenton                       0.0081231386
## countyFranklin                     0.0193224383
## countyGrant                        0.0432144665
## countyUmatilla                     0.0193224383
## damagecauseFrost:countyUmatilla    0.0211319984
## damagecauseFrost:countyWalla Walla 0.0027298561


FIGURE 14: Apples binomal model summary


Now subset to just those APPLES observations with a loss greater than zero (so all non-zeros), and run a linear regression (switched to log loss due to outliers), to make sure that our residuals and other parameters suggest normality.

## Linear mixed model fit by REML ['lmerMod']
## Formula: log(loss) ~ year + damagecause + (1 | county)
##    Data: subset(alllevs2_apples, non_zero == 1)
## 
## REML criterion at convergence: 880.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.6105 -0.5834  0.1296  0.6039  3.2595 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  county   (Intercept) 0.4085   0.6391  
##  Residual             1.9353   1.3912  
## Number of obs: 252, groups:  county, 7
## 
## Fixed effects:
##                        Estimate Std. Error t value
## (Intercept)             10.0015     0.4420  22.627
## year2002                -0.5154     0.4851  -1.062
## year2003                 0.7557     0.4627   1.633
## year2004                -0.8494     0.5155  -1.648
## year2005                 0.4481     0.4732   0.947
## year2006                 0.6558     0.4989   1.315
## year2007                 1.3272     0.4906   2.705
## year2008                 0.3012     0.5431   0.555
## year2009                 1.4475     0.4465   3.242
## year2010                 0.6472     0.4902   1.320
## year2011                 0.5794     0.4467   1.297
## year2012                 0.8257     0.6462   1.278
## year2013                 1.9262     0.4366   4.412
## year2014                 1.1395     0.5637   2.021
## year2015                 1.5109     0.4388   3.444
## damagecauseCold Winter  -0.9218     0.5054  -1.824
## damagecauseFreeze        0.1111     0.2829   0.393
## damagecauseFrost         0.1800     0.2760   0.652
## damagecauseHail          0.5523     0.3164   1.746
## damagecauseHeat         -0.8392     0.4382  -1.915


FIGURE 18: Apples mixed model coefficient estimates for damage cause and year.



FIGURE 19: Apples mixed model coefficient estimates for damage cause and year.


Finally, we examine the APPLES model coefficent estimates of our model output.


FIGURE 19: Apples mixed model coefficient estimates.


Finally, we exponentiate the coefficient estimates and confidence intervals for odds ratios.

##                         rn     lower      upper  estimate stderror
##  1:               year2002 0.2391268  1.4963560 0.5972832 1.624263
##  2:               year2003 0.8880306  5.1045958 2.1290275 1.588319
##  3:               year2004 0.1615692  1.1341296 0.4276712 1.674515
##  4:               year2005 0.6405065  3.8317532 1.5653805 1.605139
##  5:               year2006 0.7487014  4.9362244 1.9267112 1.646852
##  6:               year2007 1.4935220  9.5416645 3.7703541 1.633242
##  7:               year2008 0.4834832  3.7669837 1.3514624 1.721279
##  8:               year2009 1.8286407  9.8876821 4.2523722 1.562876
##  9:               year2010 0.7540950  4.8140575 1.9102689 1.632628
## 10:               year2011 0.7656987  4.1456813 1.7849411 1.563145
## 11:               year2012 0.6685715  7.7130937 2.2833762 1.908200
## 12:               year2013 3.0061651 15.6593281 6.8635179 1.547469
## 13:               year2014 1.0759561  9.0617292 3.1250736 1.757155
## 14:               year2015 1.9764019 10.3783962 4.5309969 1.550798
## 15: damagecauseCold Winter 0.1529470  1.0333582 0.3977923 1.657642
## 16:      damagecauseFreeze 0.6544157  1.9068833 1.1175112 1.327027
## 17:       damagecauseFrost 0.7104873  2.0162650 1.1972069 1.317828
## 18:        damagecauseHail 0.9559618  3.1613193 1.7373253 1.372203
## 19:        damagecauseHeat 0.1888239  0.9893675 0.4320540 1.549873


FIGURE 20: Apples mixed model odds ratios.


Hurdle Model - WHEAT

Here we run our hurdle technique for WHEAT, using a generalized linear model with a binomal function to delineate between zero and non-zero values. Given this model, Is our data normally distributed? What (if any) outliers exist? Are residuals well distributed - indicating normality?

##           llh       llhNull            G2      McFadden          r2ML 
## -1392.6347080 -1967.6122795  1149.9551430     0.2922210     0.3184041 
##          r2CU 
##     0.4357824
## 
##  Hosmer and Lemeshow goodness of fit (GOF) test
## 
## data:  alllevs2_wheat$non_zero, fitted(m1)
## X-squared = 8.0966, df = 8, p-value = 0.4241

FIGURE 12: Wheat Non-zero Goodness of fit hoslem test


Now plot this Wheat zero/non-zero bionomal model to see outliers and the zeros vs non-zeros.


FIGURE 13: Apples zero/non-zero bionomal model to see outliers and zeros values vs non-zero values.

Checking for multi collinearity

##                    GVIF  Df GVIF^(1/(2*Df))
## year                NaN  14             NaN
## damagecause         NaN   7             NaN
## county              NaN  24             NaN
## damagecause:county  NaN 168             NaN

FIGURE 14: Wheat multi-collinearity test for our binomal model.


##                                     pvalue
## year2003                      3.591447e-02
## year2006                      2.436066e-03
## year2008                      7.423814e-06
## year2009                      1.928975e-07
## year2010                      6.395700e-05
## year2012                      7.423814e-06
## year2013                      1.358972e-11
## year2014                      6.886671e-07
## year2015                      4.184055e-06
## countyAsotin                  9.075356e-03
## countyBenton                  9.075356e-03
## countyColumbia                2.261309e-02
## countyGarfield                9.075356e-03
## countyGilliam                 2.261309e-02
## countySherman                 2.261309e-02
## countyUnion                   2.261309e-02
## damagecauseHail:countyLincoln 4.935426e-02
## damagecauseHail:countyUnion   2.690240e-02


FIGURE 14: Wheat binomal model summary


Now subset to just those WHEAT observations with a loss greater than zero (so all non-zeros), and run a linear regression (switched to log loss due to outliers), to make sure that our residuals and other parameters suggest normality.

## Linear mixed model fit by REML ['lmerMod']
## Formula: log(loss) ~ year + damagecause + (1 | county)
##    Data: subset(alllevs2_wheat, non_zero == 1)
## 
## REML criterion at convergence: 7179.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.6996 -0.5892  0.0703  0.6781  2.6628 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  county   (Intercept) 0.3674   0.6061  
##  Residual             2.4149   1.5540  
## Number of obs: 1907, groups:  county, 25
## 
## Fixed effects:
##                             Estimate Std. Error t value
## (Intercept)                  7.99724    0.22116   36.16
## year2002                     0.43290    0.21176    2.04
## year2003                     0.41796    0.22225    1.88
## year2004                     0.27795    0.21310    1.30
## year2005                     0.07724    0.21910    0.35
## year2006                     0.68710    0.20185    3.40
## year2007                     1.05394    0.21526    4.90
## year2008                     1.69925    0.19843    8.56
## year2009                     2.80687    0.19683   14.26
## year2010                     1.03500    0.19983    5.18
## year2011                     1.13875    0.20808    5.47
## year2012                     1.08797    0.19821    5.49
## year2013                     1.87594    0.19346    9.70
## year2014                     2.09590    0.19745   10.61
## year2015                     2.44563    0.19867   12.31
## damagecauseCold Winter      -0.20275    0.15514   -1.31
## damagecauseDecline in Price  0.25623    0.15697    1.63
## damagecauseDrought           1.95038    0.14151   13.78
## damagecauseFreeze           -0.07762    0.15223   -0.51
## damagecauseFrost             0.50660    0.15314    3.31
## damagecauseHail              0.60254    0.17121    3.52
## damagecauseHeat              1.11373    0.14213    7.84


FIGURE 18: Wheat mixed model coefficient estimates for damage cause and year.



FIGURE 19: Wheat mixed model coefficient estimates for damage cause and year.


Finally, we examine the Wheat model coefficent estimates of our model output.


FIGURE 19: Wheat mixed model coefficient estimates.


Finally, we exponentiate the coefficient estimates and confidence intervals for odds ratios.

##                              rn      lower     upper   estimate stderror
##  1:                    year2002  1.0199348  2.329465  1.5417217 1.235853
##  2:                    year2003  0.9846293  2.342657  1.5188577 1.248884
##  3:                    year2004  0.8715275  2.000847  1.3204231 1.237505
##  4:                    year2005  0.7046120  1.655988  1.0802969 1.244960
##  5:                    year2006  1.3410884  2.946764  1.9879437 1.223669
##  6:                    year2007  1.8851679  4.364643  2.8689339 1.240181
##  7:                    year2008  3.7132215  8.051724  5.4698321 1.219491
##  8:                    year2009 11.2766504 24.299239 16.5580431 1.217541
##  9:                    year2010  1.9063633  4.156021  2.8151147 1.221200
## 10:                    year2011  2.0809961  4.684967  3.1228698 1.231308
## 11:                    year2012  2.0161733  4.367868  2.9682470 1.219224
## 12:                    year2013  4.4739001  9.514839  6.5269495 1.213436
## 13:                    year2014  5.5310440 11.948051  8.1327549 1.218291
## 14:                    year2015  7.8275618 16.990224 11.5377976 1.219778
## 15:      damagecauseCold Winter  0.6034317  1.105113  0.8164788 1.167822
## 16: damagecauseDecline in Price  0.9516170  1.755407  1.2920471 1.169963
## 17:          damagecauseDrought  5.3360108  9.266054  7.0313553 1.152010
## 18:           damagecauseFreeze  0.6878481  1.245579  0.9253126 1.164423
## 19:            damagecauseFrost  1.2314893  2.237926  1.6596402 1.165488
## 20:             damagecauseHail  1.3083016  2.550886  1.8267442 1.186738
## 21:             damagecauseHeat  2.3086575  4.018848  3.0457065 1.152731
##                              rn      lower     upper   estimate stderror


FIGURE 20: Wheat mixed model odds ratios.


Hurdle Model - BARLEY

Here we run our hurdle technique for BARLEY, using a generalized linear model with a binomal function to delineate between zero and non-zero values. Given this model, Is our data normally distributed? What (if any) outliers exist? Are residuals well distributed - indicating normality?

##           llh       llhNull            G2      McFadden          r2ML 
##  -830.2168952 -1274.2283306   888.0228708     0.3484552     0.3448349 
##          r2CU 
##     0.4906170
## 
##  Hosmer and Lemeshow goodness of fit (GOF) test
## 
## data:  alllevs2_barley$non_zero, fitted(m1)
## X-squared = 7.0557, df = 8, p-value = 0.5306

FIGURE 12: Barley Non-zero Goodness of fit hoslem test


Now plot this Barley zero/non-zero bionomal model to see outliers and the zeros vs non-zeros.


FIGURE 13: barley zero/non-zero bionomal model to see outliers and zeros values vs non-zero values.

Checking for multi collinearity

##                            GVIF  Df GVIF^(1/(2*Df))
## year               1.095000e+00  14           1.003
## damagecause        5.566929e+14   6          16.936
## county             3.703215e+30  19           6.374
## damagecause:county 1.804773e+44 114           1.564

FIGURE 14: barley multi-collinearity test for our binomal model.


##                                        pvalue
## (Intercept)                      0.0042218704
## year2003                         0.0494564652
## year2008                         0.0338124241
## year2011                         0.0342321549
## year2012                         0.0338124241
## year2013                         0.0004580656
## year2014                         0.0002584132
## year2015                         0.0001431552
## damagecauseDrought               0.0012138649
## damagecauseHeat                  0.0027620640
## countyWhitman                    0.0121281074
## damagecauseDrought:countyBenewah 0.0197675663


FIGURE 14: barley binomal model summary


Now subset to just those barley observations with a loss greater than zero (so all non-zeros), and run a linear regression (switched to log loss due to outliers), to make sure that our residuals and other parameters suggest normality.

## Linear mixed model fit by REML ['lmerMod']
## Formula: log(loss) ~ year + damagecause + (1 | county)
##    Data: subset(alllevs2_barley, non_zero == 1)
## 
## REML criterion at convergence: 2293.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.5822 -0.5317  0.1089  0.6977  2.9113 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  county   (Intercept) 0.3238   0.569   
##  Residual             2.2462   1.499   
## Number of obs: 620, groups:  county, 20
## 
## Fixed effects:
##                             Estimate Std. Error t value
## (Intercept)                  7.92934    0.38828  20.421
## year2002                    -0.10634    0.34844  -0.305
## year2003                     0.18599    0.33325   0.558
## year2004                    -0.85257    0.39113  -2.180
## year2005                    -0.04265    0.36706  -0.116
## year2006                    -0.67856    0.35936  -1.888
## year2007                     0.19545    0.34292   0.570
## year2008                     0.68248    0.33231   2.054
## year2009                    -0.26571    0.36026  -0.738
## year2010                    -0.66140    0.39697  -1.666
## year2011                     0.55102    0.42699   1.290
## year2012                     0.01274    0.33960   0.038
## year2013                     0.72816    0.32320   2.253
## year2014                     1.04415    0.32439   3.219
## year2015                     0.96512    0.32545   2.965
## damagecauseDecline in Price -0.64825    0.33577  -1.931
## damagecauseDrought           0.77748    0.28135   2.763
## damagecauseFreeze           -1.08850    0.44696  -2.435
## damagecauseFrost            -0.24419    0.31581  -0.773
## damagecauseHail             -0.01171    0.33567  -0.035
## damagecauseHeat              0.10291    0.28018   0.367


FIGURE 36: barley mixed model coefficient estimates for damage cause and year.



FIGURE 37: barley mixed model coefficient estimates for damage cause and year.


Finally, we examine the barley coefficent estimates of our model output.


FIGURE 19: barley mixed model coefficient estimates.


Finally, we exponentiate the coefficient estimates and confidence intervals for odds ratios.

##                              rn     lower     upper  estimate stderror
##  1:                    year2002 0.4584066 1.7605818 0.8991226 1.416849
##  2:                    year2003 0.6321075 2.2901168 1.2044047 1.395502
##  3:                    year2004 0.2004571 0.9074481 0.4263185 1.478646
##  4:                    year2005 0.4717765 1.9461020 0.9582494 1.443487
##  5:                    year2006 0.2532232 1.0145485 0.5073495 1.432413
##  6:                    year2007 0.6270592 2.3565104 1.2158574 1.409051
##  7:                    year2008 1.0416272 3.7573689 1.9787809 1.394188
##  8:                    year2009 0.3822009 1.5360223 0.7666618 1.433706
##  9:                    year2010 0.2396960 1.1099469 0.5161300 1.487307
## 10:                    year2011 0.7609116 3.9557706 1.7350299 1.532637
## 11:                    year2012 0.5242805 1.9495624 1.0128235 1.404386
## 12:                    year2013 1.1092485 3.8636135 2.0712759 1.381541
## 13:                    year2014 1.5155203 5.3101823 2.8409961 1.383185
## 14:                    year2015 1.3982636 4.9167324 2.6250936 1.384655
## 15: damagecauseDecline in Price 0.2736152 1.0003041 0.5229615 1.399019
## 16:          damagecauseDrought 1.2645497 3.7467576 2.1759737 1.324912
## 17:           damagecauseFreeze 0.1420929 0.7978644 0.3367214 1.563556
## 18:            damagecauseFrost 0.4260330 1.4421351 0.7833419 1.371369
## 19:             damagecauseHail 0.5173943 1.8921438 0.9883601 1.398874
## 20:             damagecauseHeat 0.6456397 1.9046675 1.1083912 1.323372

Hurdle Model - CHERRIES

Here we run our hurdle technique for CHERRIES, using a generalized linear model with a binomal function to delineate between zero and non-zero values. Given this model, Is our data normally distributed? What (if any) outliers exist? Are residuals well distributed - indicating normality?

##          llh      llhNull           G2     McFadden         r2ML 
## -317.8075409 -487.9400087  340.2649356    0.3486750    0.3705731 
##         r2CU 
##    0.5042351
## 
##  Hosmer and Lemeshow goodness of fit (GOF) test
## 
## data:  alllevs2_cherries$non_zero, fitted(m1)
## X-squared = 20.237, df = 8, p-value = 0.009476

FIGURE 12: Cherries Non-zero Goodness of fit hoslem test


Now plot this Cherries zero/non-zero bionomal model to see outliers and the zeros vs non-zeros.


FIGURE 13: Cherries zero/non-zero bionomal model to see outliers and zeros values vs non-zero values.

Checking for multi collinearity

##                            GVIF Df GVIF^(1/(2*Df))
## year               1.234000e+00 14           1.008
## damagecause        8.692688e+04  6           2.580
## county             3.305766e+04  6           2.380
## damagecause:county 5.530000e+08 36           1.323

FIGURE 14: Cherries multi-collinearity test for our binomal model.


##                                                     pvalue
## year2002                                      3.815859e-02
## year2005                                      1.078964e-02
## year2007                                      2.057694e-02
## year2008                                      5.511963e-03
## year2009                                      1.960629e-06
## year2010                                      3.116683e-07
## year2011                                      1.354410e-04
## year2012                                      1.960629e-06
## year2013                                      1.204504e-07
## year2014                                      1.135127e-05
## year2015                                      2.202546e-09
## damagecauseCold Winter                        1.681518e-04
## damagecauseDecline in Price                   4.792657e-03
## damagecauseHail                               1.380223e-02
## damagecauseHeat                               4.739288e-04
## countyDouglas                                 3.612953e-02
## countyWalla Walla                             1.532929e-03
## countyWasco                                   1.380223e-02
## damagecauseHeat:countyGrant                   3.199587e-02
## damagecauseDecline in Price:countyWalla Walla 4.255465e-02
## damagecauseHail:countyWalla Walla             3.705870e-02
## damagecauseCold Winter:countyWasco            1.761933e-02


FIGURE 14: Cherries binomal model summary


Now subset to just those Cherries observations with a loss greater than zero (so all non-zeros), and run a linear regression (switched to log loss due to outliers), to make sure that our residuals and other parameters suggest normality.

## Linear mixed model fit by REML ['lmerMod']
## Formula: log(loss) ~ year + damagecause + (1 | county)
##    Data: subset(alllevs2_cherries, non_zero == 1)
## 
## REML criterion at convergence: 948
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.5506 -0.5865  0.1251  0.6044  2.5611 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  county   (Intercept) 0.1767   0.4203  
##  Residual             1.7597   1.3265  
## Number of obs: 279, groups:  county, 7
## 
## Fixed effects:
##                             Estimate Std. Error t value
## (Intercept)                   8.8975     0.6014  14.794
## year2002                      0.4859     0.6666   0.729
## year2003                     -0.2252     0.6993  -0.322
## year2004                      0.3002     0.6823   0.440
## year2005                      0.7762     0.6516   1.191
## year2006                      0.2667     0.7449   0.358
## year2007                      1.3422     0.6609   2.031
## year2008                      1.8676     0.6515   2.867
## year2009                      2.2442     0.6122   3.666
## year2010                      1.8473     0.6089   3.034
## year2011                      1.7326     0.6319   2.742
## year2012                      1.3609     0.6121   2.223
## year2013                      1.8619     0.6059   3.073
## year2014                      1.4657     0.6231   2.353
## year2015                      1.6261     0.6012   2.705
## damagecauseCold Winter       -0.8428     0.4203  -2.005
## damagecauseDecline in Price  -0.7787     0.3262  -2.387
## damagecauseFreeze             0.2005     0.2504   0.801
## damagecauseFrost              0.2548     0.2463   1.034
## damagecauseHail              -0.1646     0.3335  -0.493
## damagecauseHeat              -0.1494     0.3562  -0.419


FIGURE 36: Cherries mixed model coefficient estimates for damage cause and year.



FIGURE 37: Cherries mixed model coefficient estimates for damage cause and year.


Finally, we examine the CHERRIES coefficent estimates of our model output.


FIGURE 19: Cherries mixed model coefficient estimates.


Finally, we exponentiate the coefficient estimates and confidence intervals for odds ratios.

##                              rn     lower      upper  estimate stderror
##  1:                    year2002 0.4579564  5.7241649 1.6256831 1.947578
##  2:                    year2003 0.2114117  2.9908863 0.7983585 2.012342
##  3:                    year2004 0.3693361  4.8986198 1.3501489 1.978472
##  4:                    year2005 0.6318880  7.4534131 2.1732859 1.918605
##  5:                    year2006 0.3177707  5.3375694 1.3055893 2.106231
##  6:                    year2007 1.0841355 13.3103324 3.8275486 1.936572
##  7:                    year2008 1.8709743 22.1246612 6.4724737 1.918374
##  8:                    year2009 2.9385413 29.9419903 9.4329147 1.844500
##  9:                    year2010 1.9845527 19.9962618 6.3427459 1.838396
## 10:                    year2011 1.6896045 18.6131204 5.6554231 1.881220
## 11:                    year2012 1.2072879 12.3600508 3.8996338 1.844241
## 12:                    year2013 2.0259930 20.1784870 6.4361657 1.832928
## 13:                    year2014 1.3239984 14.0376305 4.3307515 1.864617
## 14:                    year2015 1.6110876 15.7936317 5.0842582 1.824390
## 15:      damagecauseCold Winter 0.1942672  0.9539478 0.4305199 1.522409
## 16: damagecauseDecline in Price 0.2478992  0.8533862 0.4589818 1.385738
## 17:           damagecauseFreeze 0.7610356  1.9642748 1.2219719 1.284503
## 18:            damagecauseFrost 0.8103128  2.0604915 1.2901959 1.279313
## 19:             damagecauseHail 0.4523570  1.6032650 0.8482521 1.395835
## 20:             damagecauseHeat 0.4394820  1.6949052 0.8612501 1.427956

Hurdle Model - DRY PEAS

Here we run our hurdle technique for DRY PEAS, using a generalized linear model with a binomal function to delineate between zero and non-zero values. Given this model, Is our data normally distributed? What (if any) outliers exist? Are residuals well distributed - indicating normality?

##           llh       llhNull            G2      McFadden          r2ML 
##  -679.8268582 -1138.2908423   916.9279682     0.4027652     0.3620367 
##          r2CU 
##     0.5384221
## 
##  Hosmer and Lemeshow goodness of fit (GOF) test
## 
## data:  alllevs2_drypeas$non_zero, fitted(m1)
## X-squared = 9.2597, df = 8, p-value = 0.3209

FIGURE 12: Dry Peas Non-zero Goodness of fit hoslem test


Now plot this Dry Peas zero/non-zero bionomal model to see outliers and the zeros vs non-zeros.


FIGURE 13: Dry Peas zero/non-zero bionomal model to see outliers and zeros values vs non-zero values.

Checking for multi collinearity

##                    GVIF  Df GVIF^(1/(2*Df))
## year                NaN  14             NaN
## damagecause         NaN   7             NaN
## county              NaN  16             NaN
## damagecause:county  NaN 112             NaN

FIGURE 14: Dry Peas multi-collinearity test for our binomal model.


## 
## Call:
## glm(formula = non_zero ~ year + damagecause * county, family = binomial(link = logit), 
##     data = alllevs2_drypeas)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -2.35061  -0.56960  -0.20076  -0.00002   2.86220  
## 
## Coefficients:
##                                                 Estimate Std. Error
## (Intercept)                                   -3.894e+00  1.104e+00
## year2002                                       4.163e-01  4.093e-01
## year2003                                       5.682e-01  4.052e-01
## year2004                                      -1.251e+00  4.957e-01
## year2005                                       9.201e-01  3.971e-01
## year2006                                       1.179e+00  3.924e-01
## year2007                                       6.416e-01  4.033e-01
## year2008                                       1.422e+00  3.890e-01
## year2009                                       7.133e-01  4.016e-01
## year2010                                       1.654e+00  3.865e-01
## year2011                                      -1.850e-01  4.304e-01
## year2012                                       7.133e-01  4.016e-01
## year2013                                       1.985e+00  3.845e-01
## year2014                                       2.412e+00  3.847e-01
## year2015                                       2.359e+00  3.845e-01
## damagecauseCold Winter                        -1.686e+01  2.614e+03
## damagecauseDecline in Price                   -1.686e+01  2.614e+03
## damagecauseDrought                             2.158e+00  1.216e+00
## damagecauseFreeze                             -1.686e+01  2.614e+03
## damagecauseFrost                              -1.686e+01  2.614e+03
## damagecauseHail                                8.209e-01  1.325e+00
## damagecauseHeat                                1.787e+00  1.233e+00
## countyBenewah                                  2.497e+00  1.207e+00
## countyClearwater                               5.266e-14  1.500e+00
## countyColumbia                                 4.326e-14  1.500e+00
## countyGarfield                                 2.547e-14  1.500e+00
## countyGrant                                    6.770e-14  1.500e+00
## countyIdaho                                    1.787e+00  1.233e+00
## countyKootenai                                 1.787e+00  1.233e+00
## countyLatah                                    2.497e+00  1.207e+00
## countyLewis                                    3.462e+00  1.208e+00
## countyLincoln                                 -1.686e+01  2.614e+03
## countyNez Perce                                2.158e+00  1.216e+00
## countySpokane                                  2.158e+00  1.216e+00
## countyUmatilla                                 3.461e-14  1.500e+00
## countyUnion                                   -1.686e+01  2.614e+03
## countyWalla Walla                              1.360e+00  1.263e+00
## countyWhitman                                  4.180e+00  1.238e+00
## damagecauseCold Winter:countyBenewah          -2.497e+00  3.697e+03
## damagecauseDecline in Price:countyBenewah      1.518e+01  2.614e+03
## damagecauseDrought:countyBenewah              -1.192e+00  1.462e+00
## damagecauseFreeze:countyBenewah                1.436e+01  2.614e+03
## damagecauseFrost:countyBenewah                 1.615e+01  2.614e+03
## damagecauseHail:countyBenewah                 -1.531e+00  1.574e+00
## damagecauseHeat:countyBenewah                 -8.216e-01  1.476e+00
## damagecauseCold Winter:countyClearwater        6.998e-08  3.697e+03
## damagecauseDecline in Price:countyClearwater   1.822e+01  2.614e+03
## damagecauseDrought:countyClearwater            2.022e+00  1.733e+00
## damagecauseFreeze:countyClearwater            -1.838e-07  3.697e+03
## damagecauseFrost:countyClearwater              1.686e+01  2.614e+03
## damagecauseHail:countyClearwater               5.389e-01  1.830e+00
## damagecauseHeat:countyClearwater               3.705e-01  1.731e+00
## damagecauseCold Winter:countyColumbia          1.686e+01  2.614e+03
## damagecauseDecline in Price:countyColumbia     1.822e+01  2.614e+03
## damagecauseDrought:countyColumbia              1.647e+00  1.720e+00
## damagecauseFreeze:countyColumbia               1.686e+01  2.614e+03
## damagecauseFrost:countyColumbia                1.686e+01  2.614e+03
## damagecauseHail:countyColumbia                 5.389e-01  1.830e+00
## damagecauseHeat:countyColumbia                 2.017e+00  1.732e+00
## damagecauseCold Winter:countyGarfield          7.002e-08  3.697e+03
## damagecauseDecline in Price:countyGarfield     1.768e+01  2.614e+03
## damagecauseDrought:countyGarfield             -7.980e-01  1.753e+00
## damagecauseFreeze:countyGarfield              -1.837e-07  3.697e+03
## damagecauseFrost:countyGarfield                3.264e-08  3.697e+03
## damagecauseHail:countyGarfield                -1.768e+01  2.614e+03
## damagecauseHeat:countyGarfield                 7.097e-01  1.724e+00
## damagecauseCold Winter:countyGrant             6.999e-08  3.697e+03
## damagecauseDecline in Price:countyGrant        1.453e-09  3.697e+03
## damagecauseDrought:countyGrant                -1.902e+01  2.614e+03
## damagecauseFreeze:countyGrant                 -1.838e-07  3.697e+03
## damagecauseFrost:countyGrant                   1.822e+01  2.614e+03
## damagecauseHail:countyGrant                   -8.209e-01  2.001e+00
## damagecauseHeat:countyGrant                   -6.521e-14  1.743e+00
## damagecauseCold Winter:countyIdaho             1.589e+01  2.614e+03
## damagecauseDecline in Price:countyIdaho        1.589e+01  2.614e+03
## damagecauseDrought:countyIdaho                -1.407e-01  1.492e+00
## damagecauseFreeze:countyIdaho                 -1.787e+00  3.697e+03
## damagecauseFrost:countyIdaho                   1.589e+01  2.614e+03
## damagecauseHail:countyIdaho                    5.302e-01  1.571e+00
## damagecauseHeat:countyIdaho                   -1.120e-01  1.498e+00
## damagecauseCold Winter:countyKootenai         -1.787e+00  3.697e+03
## damagecauseDecline in Price:countyKootenai    -1.787e+00  3.697e+03
## damagecauseDrought:countyKootenai             -2.585e+00  1.530e+00
## damagecauseFreeze:countyKootenai              -1.787e+00  3.697e+03
## damagecauseFrost:countyKootenai                1.507e+01  2.614e+03
## damagecauseHail:countyKootenai                -1.947e+01  2.614e+03
## damagecauseHeat:countyKootenai                -1.417e+00  1.505e+00
## damagecauseCold Winter:countyLatah             1.518e+01  2.614e+03
## damagecauseDecline in Price:countyLatah        1.572e+01  2.614e+03
## damagecauseDrought:countyLatah                 5.184e-01  1.569e+00
## damagecauseFreeze:countyLatah                  1.615e+01  2.614e+03
## damagecauseFrost:countyLatah                   1.652e+01  2.614e+03
## damagecauseHail:countyLatah                   -8.209e-01  1.554e+00
## damagecauseHeat:countyLatah                    3.331e-01  1.527e+00
## damagecauseCold Winter:countyLewis             1.476e+01  2.614e+03
## damagecauseDecline in Price:countyLewis        1.476e+01  2.614e+03
## damagecauseDrought:countyLewis                -1.003e+00  1.514e+00
## damagecauseFreeze:countyLewis                  1.340e+01  2.614e+03
## damagecauseFrost:countyLewis                   1.476e+01  2.614e+03
## damagecauseHail:countyLewis                   -1.787e+00  1.554e+00
## damagecauseHeat:countyLewis                   -7.671e-02  1.582e+00
## damagecauseCold Winter:countyLincoln           3.372e+01  3.697e+03
## damagecauseDecline in Price:countyLincoln      3.454e+01  3.697e+03
## damagecauseDrought:countyLincoln               1.649e+01  2.614e+03
## damagecauseFreeze:countyLincoln                3.372e+01  3.697e+03
## damagecauseFrost:countyLincoln                 1.686e+01  4.528e+03
## damagecauseHail:countyLincoln                 -8.209e-01  3.697e+03
## damagecauseHeat:countyLincoln                  1.643e+01  2.614e+03
## damagecauseCold Winter:countyNez Perce         1.552e+01  2.614e+03
## damagecauseDecline in Price:countyNez Perce    1.606e+01  2.614e+03
## damagecauseDrought:countyNez Perce             3.018e-01  1.521e+00
## damagecauseFreeze:countyNez Perce              1.606e+01  2.614e+03
## damagecauseFrost:countyNez Perce               1.649e+01  2.614e+03
## damagecauseHail:countyNez Perce               -1.587e-01  1.558e+00
## damagecauseHeat:countyNez Perce                6.723e-01  1.535e+00
## damagecauseCold Winter:countySpokane          -2.158e+00  3.697e+03
## damagecauseDecline in Price:countySpokane      1.606e+01  2.614e+03
## damagecauseDrought:countySpokane               8.575e-01  1.576e+00
## damagecauseFreeze:countySpokane                1.552e+01  2.614e+03
## damagecauseFrost:countySpokane                 1.606e+01  2.614e+03
## damagecauseHail:countySpokane                 -8.209e-01  1.568e+00
## damagecauseHeat:countySpokane                  2.351e-01  1.507e+00
## damagecauseCold Winter:countyUmatilla          6.999e-08  3.697e+03
## damagecauseDecline in Price:countyUmatilla     1.440e-09  3.697e+03
## damagecauseDrought:countyUmatilla              6.622e-01  1.709e+00
## damagecauseFreeze:countyUmatilla               1.768e+01  2.614e+03
## damagecauseFrost:countyUmatilla                1.822e+01  2.614e+03
## damagecauseHail:countyUmatilla                -8.209e-01  2.001e+00
## damagecauseHeat:countyUmatilla                 1.675e+00  1.725e+00
## damagecauseCold Winter:countyUnion             3.372e+01  3.697e+03
## damagecauseDecline in Price:countyUnion        1.686e+01  4.528e+03
## damagecauseDrought:countyUnion                -2.158e+00  3.697e+03
## damagecauseFreeze:countyUnion                  1.686e+01  4.528e+03
## damagecauseFrost:countyUnion                   3.508e+01  3.697e+03
## damagecauseHail:countyUnion                    1.740e+01  2.614e+03
## damagecauseHeat:countyUnion                    1.686e+01  2.614e+03
## damagecauseCold Winter:countyWalla Walla      -1.360e+00  3.697e+03
## damagecauseDecline in Price:countyWalla Walla  1.686e+01  2.614e+03
## damagecauseDrought:countyWalla Walla          -5.503e-02  1.509e+00
## damagecauseFreeze:countyWalla Walla            1.632e+01  2.614e+03
## damagecauseFrost:countyWalla Walla             1.632e+01  2.614e+03
## damagecauseHail:countyWalla Walla             -2.295e-02  1.605e+00
## damagecauseHeat:countyWalla Walla              1.470e+00  1.573e+00
## damagecauseCold Winter:countyWhitman           1.447e+01  2.614e+03
## damagecauseDecline in Price:countyWhitman      1.404e+01  2.614e+03
## damagecauseDrought:countyWhitman              -1.165e+00  1.591e+00
## damagecauseFreeze:countyWhitman                1.268e+01  2.614e+03
## damagecauseFrost:countyWhitman                 1.484e+01  2.614e+03
## damagecauseHail:countyWhitman                 -1.538e+00  1.577e+00
## damagecauseHeat:countyWhitman                 -1.350e+00  1.550e+00
##                                               z value Pr(>|z|)    
## (Intercept)                                    -3.527 0.000420 ***
## year2002                                        1.017 0.309124    
## year2003                                        1.402 0.160813    
## year2004                                       -2.523 0.011643 *  
## year2005                                        2.317 0.020501 *  
## year2006                                        3.004 0.002664 ** 
## year2007                                        1.591 0.111684    
## year2008                                        3.656 0.000256 ***
## year2009                                        1.776 0.075696 .  
## year2010                                        4.278 1.88e-05 ***
## year2011                                       -0.430 0.667327    
## year2012                                        1.776 0.075696 .  
## year2013                                        5.163 2.44e-07 ***
## year2014                                        6.269 3.63e-10 ***
## year2015                                        6.135 8.53e-10 ***
## damagecauseCold Winter                         -0.006 0.994854    
## damagecauseDecline in Price                    -0.006 0.994854    
## damagecauseDrought                              1.775 0.075951 .  
## damagecauseFreeze                              -0.006 0.994854    
## damagecauseFrost                               -0.006 0.994854    
## damagecauseHail                                 0.620 0.535559    
## damagecauseHeat                                 1.450 0.147070    
## countyBenewah                                   2.069 0.038535 *  
## countyClearwater                                0.000 1.000000    
## countyColumbia                                  0.000 1.000000    
## countyGarfield                                  0.000 1.000000    
## countyGrant                                     0.000 1.000000    
## countyIdaho                                     1.450 0.147070    
## countyKootenai                                  1.450 0.147070    
## countyLatah                                     2.069 0.038535 *  
## countyLewis                                     2.865 0.004165 ** 
## countyLincoln                                  -0.006 0.994854    
## countyNez Perce                                 1.775 0.075951 .  
## countySpokane                                   1.775 0.075951 .  
## countyUmatilla                                  0.000 1.000000    
## countyUnion                                    -0.006 0.994854    
## countyWalla Walla                               1.077 0.281667    
## countyWhitman                                   3.377 0.000732 ***
## damagecauseCold Winter:countyBenewah           -0.001 0.999461    
## damagecauseDecline in Price:countyBenewah       0.006 0.995366    
## damagecauseDrought:countyBenewah               -0.815 0.414808    
## damagecauseFreeze:countyBenewah                 0.005 0.995616    
## damagecauseFrost:countyBenewah                  0.006 0.995071    
## damagecauseHail:countyBenewah                  -0.972 0.330959    
## damagecauseHeat:countyBenewah                  -0.557 0.577764    
## damagecauseCold Winter:countyClearwater         0.000 1.000000    
## damagecauseDecline in Price:countyClearwater    0.007 0.994439    
## damagecauseDrought:countyClearwater             1.167 0.243350    
## damagecauseFreeze:countyClearwater              0.000 1.000000    
## damagecauseFrost:countyClearwater               0.006 0.994854    
## damagecauseHail:countyClearwater                0.294 0.768463    
## damagecauseHeat:countyClearwater                0.214 0.830481    
## damagecauseCold Winter:countyColumbia           0.006 0.994854    
## damagecauseDecline in Price:countyColumbia      0.007 0.994439    
## damagecauseDrought:countyColumbia               0.957 0.338470    
## damagecauseFreeze:countyColumbia                0.006 0.994854    
## damagecauseFrost:countyColumbia                 0.006 0.994854    
## damagecauseHail:countyColumbia                  0.294 0.768463    
## damagecauseHeat:countyColumbia                  1.164 0.244299    
## damagecauseCold Winter:countyGarfield           0.000 1.000000    
## damagecauseDecline in Price:countyGarfield      0.007 0.994604    
## damagecauseDrought:countyGarfield              -0.455 0.648911    
## damagecauseFreeze:countyGarfield                0.000 1.000000    
## damagecauseFrost:countyGarfield                 0.000 1.000000    
## damagecauseHail:countyGarfield                 -0.007 0.994604    
## damagecauseHeat:countyGarfield                  0.412 0.680639    
## damagecauseCold Winter:countyGrant              0.000 1.000000    
## damagecauseDecline in Price:countyGrant         0.000 1.000000    
## damagecauseDrought:countyGrant                 -0.007 0.994196    
## damagecauseFreeze:countyGrant                   0.000 1.000000    
## damagecauseFrost:countyGrant                    0.007 0.994439    
## damagecauseHail:countyGrant                    -0.410 0.681693    
## damagecauseHeat:countyGrant                     0.000 1.000000    
## damagecauseCold Winter:countyIdaho              0.006 0.995149    
## damagecauseDecline in Price:countyIdaho         0.006 0.995149    
## damagecauseDrought:countyIdaho                 -0.094 0.924867    
## damagecauseFreeze:countyIdaho                   0.000 0.999614    
## damagecauseFrost:countyIdaho                    0.006 0.995149    
## damagecauseHail:countyIdaho                     0.337 0.735788    
## damagecauseHeat:countyIdaho                    -0.075 0.940408    
## damagecauseCold Winter:countyKootenai           0.000 0.999614    
## damagecauseDecline in Price:countyKootenai      0.000 0.999614    
## damagecauseDrought:countyKootenai              -1.689 0.091178 .  
## damagecauseFreeze:countyKootenai                0.000 0.999614    
## damagecauseFrost:countyKootenai                 0.006 0.995400    
## damagecauseHail:countyKootenai                 -0.007 0.994058    
## damagecauseHeat:countyKootenai                 -0.942 0.346419    
## damagecauseCold Winter:countyLatah              0.006 0.995366    
## damagecauseDecline in Price:countyLatah         0.006 0.995201    
## damagecauseDrought:countyLatah                  0.330 0.741127    
## damagecauseFreeze:countyLatah                   0.006 0.995071    
## damagecauseFrost:countyLatah                    0.006 0.994958    
## damagecauseHail:countyLatah                    -0.528 0.597231    
## damagecauseHeat:countyLatah                     0.218 0.827319    
## damagecauseCold Winter:countyLewis              0.006 0.995496    
## damagecauseDecline in Price:countyLewis         0.006 0.995496    
## damagecauseDrought:countyLewis                 -0.663 0.507626    
## damagecauseFreeze:countyLewis                   0.005 0.995911    
## damagecauseFrost:countyLewis                    0.006 0.995496    
## damagecauseHail:countyLewis                    -1.149 0.250436    
## damagecauseHeat:countyLewis                    -0.048 0.961340    
## damagecauseCold Winter:countyLincoln            0.009 0.992723    
## damagecauseDecline in Price:countyLincoln       0.009 0.992546    
## damagecauseDrought:countyLincoln                0.006 0.994967    
## damagecauseFreeze:countyLincoln                 0.009 0.992723    
## damagecauseFrost:countyLincoln                  0.004 0.997029    
## damagecauseHail:countyLincoln                   0.000 0.999823    
## damagecauseHeat:countyLincoln                   0.006 0.994985    
## damagecauseCold Winter:countyNez Perce          0.006 0.995262    
## damagecauseDecline in Price:countyNez Perce     0.006 0.995098    
## damagecauseDrought:countyNez Perce              0.198 0.842734    
## damagecauseFreeze:countyNez Perce               0.006 0.995098    
## damagecauseFrost:countyNez Perce                0.006 0.994967    
## damagecauseHail:countyNez Perce                -0.102 0.918856    
## damagecauseHeat:countyNez Perce                 0.438 0.661340    
## damagecauseCold Winter:countySpokane           -0.001 0.999534    
## damagecauseDecline in Price:countySpokane       0.006 0.995098    
## damagecauseDrought:countySpokane                0.544 0.586466    
## damagecauseFreeze:countySpokane                 0.006 0.995262    
## damagecauseFrost:countySpokane                  0.006 0.995098    
## damagecauseHail:countySpokane                  -0.523 0.600637    
## damagecauseHeat:countySpokane                   0.156 0.876061    
## damagecauseCold Winter:countyUmatilla           0.000 1.000000    
## damagecauseDecline in Price:countyUmatilla      0.000 1.000000    
## damagecauseDrought:countyUmatilla               0.387 0.698416    
## damagecauseFreeze:countyUmatilla                0.007 0.994604    
## damagecauseFrost:countyUmatilla                 0.007 0.994439    
## damagecauseHail:countyUmatilla                 -0.410 0.681693    
## damagecauseHeat:countyUmatilla                  0.971 0.331477    
## damagecauseCold Winter:countyUnion              0.009 0.992723    
## damagecauseDecline in Price:countyUnion         0.004 0.997029    
## damagecauseDrought:countyUnion                 -0.001 0.999534    
## damagecauseFreeze:countyUnion                   0.004 0.997029    
## damagecauseFrost:countyUnion                    0.009 0.992429    
## damagecauseHail:countyUnion                     0.007 0.994690    
## damagecauseHeat:countyUnion                     0.006 0.994854    
## damagecauseCold Winter:countyWalla Walla        0.000 0.999707    
## damagecauseDecline in Price:countyWalla Walla   0.006 0.994854    
## damagecauseDrought:countyWalla Walla           -0.036 0.970915    
## damagecauseFreeze:countyWalla Walla             0.006 0.995019    
## damagecauseFrost:countyWalla Walla              0.006 0.995019    
## damagecauseHail:countyWalla Walla              -0.014 0.988596    
## damagecauseHeat:countyWalla Walla               0.935 0.349923    
## damagecauseCold Winter:countyWhitman            0.006 0.995584    
## damagecauseDecline in Price:countyWhitman       0.005 0.995715    
## damagecauseDrought:countyWhitman               -0.732 0.464127    
## damagecauseFreeze:countyWhitman                 0.005 0.996130    
## damagecauseFrost:countyWhitman                  0.006 0.995471    
## damagecauseHail:countyWhitman                  -0.975 0.329327    
## damagecauseHeat:countyWhitman                  -0.871 0.383744    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2276.6  on 2039  degrees of freedom
## Residual deviance: 1359.7  on 1890  degrees of freedom
## AIC: 1659.7
## 
## Number of Fisher Scoring iterations: 18


FIGURE 14: Dry Peas binomal model summary


Now subset to just those Dry Peas observations with a loss greater than zero (so all non-zeros), and run a linear regression (switched to log loss due to outliers), to make sure that our residuals and other parameters suggest normality.

## Linear mixed model fit by REML ['lmerMod']
## Formula: log(loss) ~ year + damagecause + (1 | county)
##    Data: subset(alllevs2_drypeas, non_zero == 1)
## 
## REML criterion at convergence: 1860
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9544 -0.4928  0.1551  0.6655  2.1097 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  county   (Intercept) 0.3996   0.6321  
##  Residual             2.2811   1.5103  
## Number of obs: 502, groups:  county, 17
## 
## Fixed effects:
##                             Estimate Std. Error t value
## (Intercept)                   6.4011     0.4337  14.758
## year2002                      1.1477     0.4605   2.492
## year2003                      1.7577     0.4493   3.912
## year2004                      1.6750     0.6272   2.670
## year2005                      2.2060     0.4360   5.059
## year2006                      1.3581     0.4271   3.180
## year2007                      1.6262     0.4486   3.625
## year2008                      2.4535     0.4210   5.828
## year2009                      1.8246     0.4456   4.095
## year2010                      2.3902     0.4191   5.703
## year2011                      2.0400     0.5166   3.949
## year2012                      2.2563     0.4510   5.003
## year2013                      2.4718     0.4136   5.977
## year2014                      2.9396     0.4059   7.243
## year2015                      3.8526     0.4023   9.577
## damagecauseCold Winter       -0.6207     0.4355  -1.425
## damagecauseDecline in Price  -0.4614     0.3677  -1.255
## damagecauseDrought            0.4783     0.2587   1.849
## damagecauseFreeze            -0.9689     0.4255  -2.277
## damagecauseFrost             -0.2361     0.3297  -0.716
## damagecauseHail               0.3804     0.2905   1.309
## damagecauseHeat               0.2298     0.2515   0.914


FIGURE 45: Dry Peas mixed model coefficient estimates for damage cause and year.



FIGURE 46: Dry Peas mixed model coefficient estimates for damage cause and year.


Finally, we examine the DRY PEAS coefficent estimates of our model output.


FIGURE 47: Dry Peas mixed model coefficient estimates for damage cause and year.


FIGURE 19: Dry Peas mixed model coefficient estimates.


Finally, we exponentiate the coefficient estimates and confidence intervals for odds ratios.

##                              rn      lower       upper   estimate stderror
##  1:                    year2002  1.3017723   7.6412632  3.1510220 1.584912
##  2:                    year2003  2.4469410  13.7523548  5.7990471 1.567200
##  3:                    year2004  1.6018655  17.8527384  5.3388800 1.872447
##  4:                    year2005  3.9293215  20.9850703  9.0796703 1.546574
##  5:                    year2006  1.7129457   8.8396657  3.8887481 1.532749
##  6:                    year2007  2.1497273  12.0563155  5.0844397 1.566053
##  7:                    year2008  5.1830773  26.1285021 11.6295078 1.523426
##  8:                    year2009  2.6352492  14.5996543  6.2000068 1.561365
##  9:                    year2010  4.8811790  24.4259125 10.9157261 1.520577
## 10:                    year2011  2.8537106  20.8210658  7.6903393 1.676387
## 11:                    year2012  4.0176232  22.7341095  9.5473067 1.569822
## 12:                    year2013  5.3546238  26.2384348 11.8432900 1.512191
## 13:                    year2014  8.6741820  41.2573245 18.9087670 1.500614
## 14:                    year2015 21.7649829 102.1191780 47.1175633 1.495241
## 15:      damagecauseCold Winter  0.2330977   1.2458334  0.5375878 1.545689
## 16: damagecauseDecline in Price  0.3109437   1.2771526  0.6304087 1.444388
## 17:          damagecauseDrought  0.9812936   2.6511404  1.6132606 1.295214
## 18:           damagecauseFreeze  0.1677002   0.8607936  0.3795095 1.530426
## 19:            damagecauseFrost  0.4194035   1.4890046  0.7897253 1.390562
## 20:             damagecauseHail  0.8377201   2.5599627  1.4629353 1.337147
## 21:             damagecauseHeat  0.7758169   2.0391972  1.2582955 1.285938
##                              rn      lower       upper   estimate stderror